% Mizar problem: e3_80,topalg_6,3423,35 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_80_type,type,( c1_80__topalg_6: $i )).
thf(k1_card_1_type,type,( k1_card_1: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_nat_1_type,type,( k1_nat_1: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_topalg_6_type,type,( k1_topalg_6: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_xxreal_2_type,type,( k1_xxreal_2: $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_struct_0_type,type,( k2_struct_0: $i > $i )).
thf(k2_xcmplx_0_type,type,( k2_xcmplx_0: $i > $i > $i )).
thf(k2_xxreal_2_type,type,( k2_xxreal_2: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_finseq_1_type,type,( k3_finseq_1: $i > $i )).
thf(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_numbers_type,type,( k3_numbers: $i )).
thf(k4_numbers_type,type,( k4_numbers: $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_partfun1_type,type,( k4_partfun1: $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_numbers_type,type,( k6_numbers: $i )).
thf(k6_topalg_6_type,type,( k6_topalg_6: $i > $i > $i )).
thf(k7_partfun1_type,type,( k7_partfun1: $i > $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_pre_topc_type,type,( l1_pre_topc: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(m1_finseq_1_type,type,( m1_finseq_1: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_finseq_1_type,type,( m2_finseq_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(r1_topalg_6_type,type,( r1_topalg_6: $i > $i > $i > $o )).
thf(r1_xxreal_0_type,type,( r1_xxreal_0: $i > $i > $o )).
thf(r2_topalg_6_type,type,( r2_topalg_6: $i > $i > $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_borsuk_2_type,type,( v1_borsuk_2: $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_compts_1_type,type,( v1_compts_1: $i > $o )).
thf(v1_connsp_1_type,type,( v1_connsp_1: $i > $o )).
thf(v1_finseq_1_type,type,( v1_finseq_1: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_frechet_type,type,( v1_frechet: $i > $o )).
thf(v1_funcop_1_type,type,( v1_funcop_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_membered_type,type,( v1_membered: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_tdlat_3_type,type,( v1_tdlat_3: $i > $o )).
thf(v1_topalg_6_type,type,( v1_topalg_6: $i > $o )).
thf(v1_topgrp_1_type,type,( v1_topgrp_1: $i > $o )).
thf(v1_valued_0_type,type,( v1_valued_0: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v1_xxreal_2_type,type,( v1_xxreal_2: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_connsp_1_type,type,( v2_connsp_1: $i > $i > $o )).
thf(v2_finseq_1_type,type,( v2_finseq_1: $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_funct_2_type,type,( v2_funct_2: $i > $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_mfold_1_type,type,( v2_mfold_1: $i > $i > $o )).
thf(v2_pre_topc_type,type,( v2_pre_topc: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_tdlat_3_type,type,( v2_tdlat_3: $i > $o )).
thf(v2_topalg_6_type,type,( v2_topalg_6: $i > $o )).
thf(v2_valued_0_type,type,( v2_valued_0: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v2_xxreal_2_type,type,( v2_xxreal_2: $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_finseq_1_type,type,( v3_finseq_1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_funct_2_type,type,( v3_funct_2: $i > $i > $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_valued_0_type,type,( v3_valued_0: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v3_xxreal_2_type,type,( v3_xxreal_2: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_pre_topc_type,type,( v4_pre_topc: $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_valued_0_type,type,( v4_valued_0: $i > $o )).
thf(v4_xxreal_2_type,type,( v4_xxreal_2: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_pre_topc_type,type,( v5_pre_topc: $i > $i > $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_topalg_6_type,type,( v5_topalg_6: $i > $i > $o )).
thf(v5_valued_0_type,type,( v5_valued_0: $i > $o )).
thf(v5_xxreal_2_type,type,( v5_xxreal_2: $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v6_pre_topc_type,type,( v6_pre_topc: $i > $o )).
thf(v6_topalg_6_type,type,( v6_topalg_6: $i > $i > $o )).
thf(v6_valued_0_type,type,( v6_valued_0: $i > $o )).
thf(v6_xxreal_2_type,type,( v6_xxreal_2: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v7_topalg_6_type,type,( v7_topalg_6: $i > $i > $o )).
thf(v7_valued_0_type,type,( v7_valued_0: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(v8_valued_0_type,type,( v8_valued_0: $i > $o )).
thf(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(cc15_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_rat_1 @ B ) ) ) ),file(membered,cc15_membered)).
thf(cc19_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v4_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v5_relat_1 @ C @ k3_numbers ) ) ) ),file(valued_0,cc19_valued_0)).
thf(cc22_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_membered @ B ) ) ) ),file(membered,cc22_membered)).
thf(cc2_mfold_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ! [B: $i] : ( ( l1_pre_topc @ B ) => ( ( ~ ( v2_struct_0 @ B ) & ( v2_pre_topc @ B ) & ( v2_mfold_1 @ B @ A ) ) => ( ~ ( v2_struct_0 @ B ) & ( v2_pre_topc @ B ) & ( v1_frechet @ B ) ) ) ) ) ),file(mfold_1,cc2_mfold_1)).
thf(cc2_topalg_6,axiom,( ! [A: $i] : ( ( ( v7_ordinal1 @ A ) & ( v2_xxreal_0 @ A ) ) => ! [B: $i] : ( ( l1_pre_topc @ B ) => ( ( ~ ( v2_struct_0 @ B ) & ( v2_pre_topc @ B ) & ( v2_mfold_1 @ B @ A ) ) => ( ~ ( v2_struct_0 @ B ) & ~ ( v8_struct_0 @ B ) & ( v2_pre_topc @ B ) ) ) ) ) ),file(topalg_6,cc2_topalg_6)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(cc3_mfold_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v2_mfold_1 @ A @ k1_xboole_0 ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_tdlat_3 @ A ) ) ) ) ),file(mfold_1,cc3_mfold_1)).
thf(cc3_topalg_6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v2_topalg_6 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_borsuk_2 @ A ) & ( v1_topalg_6 @ A ) ) ) ) ),file(topalg_6,cc3_topalg_6)).
thf(fc4_xxreal_2,axiom,( ! [A: $i] : ( ( ( v4_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k2_xxreal_2 @ A ) ) & ( v1_rat_1 @ ( k2_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc4_xxreal_2)).
thf(fc88_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v4_membered @ B ) => ( v5_relat_1 @ ( k2_zfmisc_1 @ A @ B ) @ k3_numbers ) ) ),file(valued_0,fc88_valued_0)).
thf(fc8_xxreal_2,axiom,( ! [A: $i] : ( ( ( v4_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k1_xxreal_2 @ A ) ) & ( v1_rat_1 @ ( k1_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc8_xxreal_2)).
thf(rc1_borsuk_2,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v5_relat_1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ B ) & ( v2_funct_1 @ B ) & ( v1_partfun1 @ B @ ( u1_struct_0 @ A ) ) & ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) & ( v5_pre_topc @ B @ A @ A ) ) ) ),file(borsuk_2,rc1_borsuk_2)).
thf(rc1_xxreal_2,axiom,( ? [A: $i] : ( ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) ) ),file(xxreal_2,rc1_xxreal_2)).
thf(rc3_mfold_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ? [B: $i] : ( ( l1_pre_topc @ B ) & ~ ( v2_struct_0 @ B ) & ( v2_pre_topc @ B ) & ( v2_mfold_1 @ B @ A ) ) ) ),file(mfold_1,rc3_mfold_1)).
thf(rc3_xxreal_2,axiom,( ? [A: $i] : ( ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v5_xxreal_2 @ A ) ) ),file(xxreal_2,rc3_xxreal_2)).
thf(rc8_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_pre_topc @ B ) & ( l1_pre_topc @ B ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ ( u1_struct_0 @ A ) ) & ( v5_relat_1 @ C @ ( u1_struct_0 @ B ) ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) & ( v5_pre_topc @ C @ A @ B ) ) ) ),file(pre_topc,rc8_pre_topc)).
thf(dt_k3_numbers,axiom,( $true ),file(numbers,k3_numbers)).
thf(dt_k4_numbers,axiom,( $true ),file(numbers,k4_numbers)).
thf(cc10_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k4_numbers ) ) => ( v5_membered @ A ) ) ),file(membered,cc10_membered)).
thf(cc10_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_valued_0 @ B ) ) ) ),file(valued_0,cc10_valued_0)).
thf(cc12_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_valued_0 @ A ) & ( v5_valued_0 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) & ( v3_valued_0 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc12_finseq_1)).
thf(cc12_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ( v1_finset_1 @ A ) ) ) ),file(xxreal_2,cc12_xxreal_2)).
thf(cc13_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_relat_1 @ B @ k3_numbers ) ) ) ),file(valued_0,cc13_valued_0)).
thf(cc14_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_relat_1 @ B @ k4_numbers ) ) ) ),file(valued_0,cc14_valued_0)).
thf(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_membered)).
thf(cc1_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ B ) & ( v2_pre_topc @ B ) & ( l1_pre_topc @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v3_funct_1 @ C ) & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) => ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) & ( v5_pre_topc @ C @ A @ B ) ) ) ) ) ),file(topalg_6,cc1_topalg_6)).
thf(cc20_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v5_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v5_relat_1 @ C @ k4_numbers ) ) ) ),file(valued_0,cc20_valued_0)).
thf(cc23_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_membered @ B ) ) ) ),file(membered,cc23_membered)).
thf(cc23_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v5_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v7_valued_0 @ A ) ) ) ),file(valued_0,cc23_valued_0)).
thf(cc24_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v6_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v8_valued_0 @ A ) ) ) ),file(valued_0,cc24_valued_0)).
thf(cc2_borsuk_2,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_borsuk_2 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_connsp_1 @ A ) ) ) ) ),file(borsuk_2,cc2_borsuk_2)).
thf(cc2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc2_funct_2)).
thf(cc2_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
thf(cc2_tex_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_tdlat_3 @ A ) & ( v2_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) & ( v2_pre_topc @ A ) ) ) ) ),file(tex_1,cc2_tex_1)).
thf(cc2_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc2_valued_0)).
thf(cc3_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( v1_finset_1 @ C ) ) ) ) ) ),file(finset_1,cc3_finset_1)).
thf(cc3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc3_funct_2)).
thf(cc3_tex_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v1_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v7_struct_0 @ A ) & ( v2_pre_topc @ A ) ) ) ) ),file(tex_1,cc3_tex_1)).
thf(cc3_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc3_valued_0)).
thf(cc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_funct_2 @ B @ A @ A ) => ( v1_partfun1 @ B @ A ) ) ) ),file(funct_2,cc4_funct_2)).
thf(cc4_mfold_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v2_mfold_1 @ A @ k1_xboole_0 ) ) ) ) ),file(mfold_1,cc4_mfold_1)).
thf(cc4_tex_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ~ ( v2_tdlat_3 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v7_struct_0 @ A ) & ( v2_pre_topc @ A ) ) ) ) ),file(tex_1,cc4_tex_1)).
thf(cc4_topalg_6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_borsuk_2 @ A ) & ( v1_topalg_6 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v2_topalg_6 @ A ) ) ) ) ),file(topalg_6,cc4_topalg_6)).
thf(cc4_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc4_valued_0)).
thf(cc5_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v3_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ( v2_funct_1 @ C ) & ( v2_funct_2 @ C @ B ) ) ) ) ),file(funct_2,cc5_funct_2)).
thf(cc7_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v2_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc7_xxreal_2)).
thf(cc8_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ~ ( v1_xboole_0 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ),file(funct_2,cc8_funct_2)).
thf(cc8_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v3_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc8_xxreal_2)).
thf(cc9_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k3_numbers ) ) => ( v4_membered @ A ) ) ),file(membered,cc9_membered)).
thf(fc3_numbers,axiom,( ~ ( v1_xboole_0 @ k3_numbers ) ),file(numbers,fc3_numbers)).
thf(fc4_membered,axiom,( v4_membered @ k3_numbers ),file(membered,fc4_membered)).
thf(fc4_numbers,axiom,( ~ ( v1_xboole_0 @ k4_numbers ) ),file(numbers,fc4_numbers)).
thf(fc57_membered,axiom,( v7_membered @ k3_numbers ),file(membered,fc57_membered)).
thf(fc58_membered,axiom,( v7_membered @ k4_numbers ),file(membered,fc58_membered)).
thf(fc5_membered,axiom,( v5_membered @ k4_numbers ),file(membered,fc5_membered)).
thf(fc5_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k2_xxreal_2 @ A ) ) & ( v1_int_1 @ ( k2_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc5_xxreal_2)).
thf(fc61_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( v1_xcmplx_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc61_valued_0)).
thf(fc64_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_rat_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc64_valued_0)).
thf(fc65_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) ) => ( v1_int_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc65_valued_0)).
thf(fc6_numbers,axiom,( ~ ( v1_finset_1 @ k4_numbers ) ),file(numbers,fc6_numbers)).
thf(fc7_numbers,axiom,( ~ ( v1_finset_1 @ k3_numbers ) ),file(numbers,fc7_numbers)).
thf(fc89_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v5_membered @ B ) => ( v5_relat_1 @ ( k2_zfmisc_1 @ A @ B ) @ k4_numbers ) ) ),file(valued_0,fc89_valued_0)).
thf(fc9_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k1_xxreal_2 @ A ) ) & ( v1_int_1 @ ( k1_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc9_xxreal_2)).
thf(rc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ),file(funct_2,rc1_funct_2)).
thf(rc1_topgrp_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v2_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_funct_2 @ B @ A @ A ) & ( v2_funct_2 @ B @ A ) ) ),file(topgrp_1,rc1_topgrp_1)).
thf(rc2_funct_2,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_funct_2 @ B @ A @ A ) & ( v3_funct_2 @ B @ A @ A ) ) ),file(funct_2,rc2_funct_2)).
thf(rc2_valued_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) & ( v5_relat_1 @ A @ k4_numbers ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc2_valued_0)).
thf(rc3_valued_0,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ k5_numbers ) ) ) & ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v5_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ k5_numbers ) & ( v1_funct_2 @ A @ k5_numbers @ k5_numbers ) & ( v1_valued_0 @ A ) & ( v2_valued_0 @ A ) & ( v3_valued_0 @ A ) & ( v4_valued_0 @ A ) & ( v5_valued_0 @ A ) ) ),file(valued_0,rc3_valued_0)).
thf(rc4_valued_0,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v3_funct_1 @ B ) & ( v1_funct_2 @ B @ k5_numbers @ A ) ) ),file(valued_0,rc4_valued_0)).
thf(rc7_finseq_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ) ),file(finseq_1,rc7_finseq_1)).
thf(ie1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k7_partfun1 @ B @ C @ D ) @ ( k3_funct_2 @ A @ B @ C @ D ) ) ) ),file(funct_2,ie1_funct_2)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(cc10_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,cc10_finseq_1)).
thf(cc10_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
thf(cc10_topalg_6,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) => ( ( v5_topalg_6 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(topalg_6,cc10_topalg_6)).
thf(cc10_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v3_membered @ A ) & ( v3_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc10_xxreal_2)).
thf(cc11_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_finseq_1 @ B ) ) ) ),file(finseq_1,cc11_finseq_1)).
thf(cc11_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ) ) ),file(struct_0,cc11_struct_0)).
thf(cc11_topalg_6,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) => ( ( v6_topalg_6 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(topalg_6,cc11_topalg_6)).
thf(cc11_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_valued_0 @ B ) ) ) ),file(valued_0,cc11_valued_0)).
thf(cc11_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v3_membered @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc11_xxreal_2)).
thf(cc12_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xcmplx_0 @ B ) ) ) ),file(membered,cc12_membered)).
thf(cc12_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_valued_0 @ B ) ) ) ),file(valued_0,cc12_valued_0)).
thf(cc13_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v6_membered @ A ) & ( v1_finset_1 @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc13_xxreal_2)).
thf(cc14_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v3_membered @ A ) ) ) ),file(xxreal_2,cc14_xxreal_2)).
thf(cc15_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_valued_0 @ B ) ) ) ),file(valued_0,cc15_valued_0)).
thf(cc16_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_valued_0 @ C ) ) ) ),file(valued_0,cc16_valued_0)).
thf(cc16_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(xxreal_2,cc16_xxreal_2)).
thf(cc17_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_membered)).
thf(cc17_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc17_struct_0)).
thf(cc17_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(xxreal_2,cc17_xxreal_2)).
thf(cc19_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_membered @ B ) ) ) ),file(membered,cc19_membered)).
thf(cc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_tex_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ( v13_struct_0 @ A @ np__1 ) & ( v2_pre_topc @ A ) ) => ( ( v13_struct_0 @ A @ np__1 ) & ( v2_pre_topc @ A ) & ( v1_tdlat_3 @ A ) & ( v2_tdlat_3 @ A ) ) ) ) ),file(tex_1,cc1_tex_1)).
thf(cc1_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k4_numbers ) ) ) ),file(valued_0,cc1_valued_0)).
thf(cc21_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v6_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v4_valued_0 @ C ) ) ) ),file(valued_0,cc21_valued_0)).
thf(cc22_valued_0,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) & ( v5_valued_0 @ A ) & ( v6_valued_0 @ A ) ) ) ),file(valued_0,cc22_valued_0)).
thf(cc24_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_membered @ B ) ) ) ),file(membered,cc24_membered)).
thf(cc2_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funcop_1 @ A ) ) ) ),file(funcop_1,cc2_funcop_1)).
thf(cc2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc2_struct_0)).
thf(cc2_topalg_3,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) & ( v2_pre_topc @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_borsuk_2 @ A ) ) ) ) ),file(topalg_3,cc2_topalg_3)).
thf(cc2_zfmisc_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(zfmisc_1,cc2_zfmisc_1)).
thf(cc3_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) => ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc3_xxreal_2)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc4_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc4_xxreal_2)).
thf(cc5_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(funct_1,cc5_funct_1)).
thf(cc5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v4_relat_1 @ C @ A ) ) ) ),file(relat_1,cc5_relat_1)).
thf(cc5_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc5_struct_0)).
thf(cc5_topalg_6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) & ( v2_pre_topc @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_topalg_6 @ A ) ) ) ) ),file(topalg_6,cc5_topalg_6)).
thf(cc5_topgrp_1,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ( v13_struct_0 @ A @ np__1 ) & ( v1_topgrp_1 @ A ) ) ) ) ),file(topgrp_1,cc5_topgrp_1)).
thf(cc5_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_valued_0 @ A ) ) ) ),file(valued_0,cc5_valued_0)).
thf(cc6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc6_funct_1)).
thf(cc6_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v2_funct_1 @ C ) & ( v2_funct_2 @ C @ B ) ) => ( ( v1_funct_1 @ C ) & ( v3_funct_2 @ C @ A @ B ) ) ) ) ),file(funct_2,cc6_funct_2)).
thf(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc6_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) ) ),file(valued_0,cc6_valued_0)).
thf(cc7_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ) ),file(finseq_1,cc7_finseq_1)).
thf(cc7_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_1)).
thf(cc7_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc7_relat_1)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc7_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k3_numbers ) ) ) ),file(valued_0,cc7_valued_0)).
thf(cc8_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_finset_1 @ B ) ) ) ),file(finset_1,cc8_finset_1)).
thf(cc8_topalg_6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) => ( ( ( v5_topalg_6 @ B @ A ) & ( v6_topalg_6 @ B @ A ) ) => ( v7_topalg_6 @ B @ A ) ) ) ) ),file(topalg_6,cc8_topalg_6)).
thf(cc8_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc8_valued_0)).
thf(cc9_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ( v4_funct_1 @ A ) ) ),file(finseq_1,cc9_finseq_1)).
thf(cc9_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ k1_xboole_0 ) => ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc9_struct_0)).
thf(cc9_xxreal_2,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( ( v6_membered @ A ) & ( v3_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc9_xxreal_2)).
thf(fc10_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) & ( v5_topalg_6 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) ) => ( ( v1_xreal_0 @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ B ) ) ) & ( v1_xxreal_0 @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ B ) ) ) ) ) ),file(topalg_6,fc10_topalg_6)).
thf(fc10_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k1_xxreal_2 @ A ) ) & ( v7_ordinal1 @ ( k1_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc10_xxreal_2)).
thf(fc11_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( m1_subset_1 @ B @ ( k9_xtuple_0 @ A ) ) ) => ~ ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc11_funct_1)).
thf(fc11_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) & ( v6_topalg_6 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ B ) ) ) ),file(topalg_6,fc11_topalg_6)).
thf(fc12_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) & ( v6_topalg_6 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) ) => ( ( v1_xreal_0 @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ B ) ) ) & ( v1_xxreal_0 @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ B ) ) ) ) ) ),file(topalg_6,fc12_topalg_6)).
thf(fc18_funct_1,axiom,( ! [A: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(funct_1,fc18_funct_1)).
thf(fc19_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc19_funct_1)).
thf(fc19_struct_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_card_1 @ A ) & ( v13_struct_0 @ B @ A ) & ( l1_struct_0 @ B ) ) => ( v3_card_1 @ ( u1_struct_0 @ B ) @ A ) ) ),file(struct_0,fc19_struct_0)).
thf(fc24_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc24_relat_1)).
thf(fc29_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v3_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( v1_finseq_1 @ ( k1_funct_1 @ B @ C ) ) ) ),file(finseq_1,fc29_finseq_1)).
thf(fc35_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) => ( v1_finset_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(finset_1,fc35_finset_1)).
thf(fc3_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k2_xxreal_2 @ A ) ) & ( v1_xreal_0 @ ( k2_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc3_xxreal_2)).
thf(fc59_membered,axiom,( v7_membered @ k4_ordinal1 ),file(membered,fc59_membered)).
thf(fc62_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_valued_0 @ A ) ) => ( v1_xxreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc62_valued_0)).
thf(fc63_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_valued_0 @ A ) ) => ( v1_xreal_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc63_valued_0)).
thf(fc66_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) => ( v7_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc66_valued_0)).
thf(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
thf(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc6_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k2_xxreal_2 @ A ) ) & ( v7_ordinal1 @ ( k2_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc6_xxreal_2)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc7_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k1_xxreal_2 @ A ) ) & ( v1_xreal_0 @ ( k1_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc7_xxreal_2)).
thf(fc85_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_membered @ B ) => ( v1_valued_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(valued_0,fc85_valued_0)).
thf(fc8_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(funcop_1,fc8_funcop_1)).
thf(fc8_struct_0,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc8_struct_0)).
thf(fc90_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v6_membered @ B ) => ( v4_valued_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(valued_0,fc90_valued_0)).
thf(fc9_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc9_struct_0)).
thf(fc9_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) & ( v5_topalg_6 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ B ) ) ) ),file(topalg_6,fc9_topalg_6)).
thf(rc1_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ),file(finseq_1,rc1_finseq_1)).
thf(rc1_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ),file(funcop_1,rc1_funcop_1)).
thf(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
thf(rc1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(partfun1,rc1_partfun1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc1_valued_0,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v4_valued_0 @ A ) ) ),file(valued_0,rc1_valued_0)).
thf(rc1_zfmisc_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,rc1_zfmisc_1)).
thf(rc21_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc21_struct_0)).
thf(rc22_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc22_struct_0)).
thf(rc23_struct_0,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( ( l1_struct_0 @ B ) & ( v13_struct_0 @ B @ A ) ) ) ),file(struct_0,rc23_struct_0)).
thf(rc2_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_finseq_1 @ B @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) ) ),file(finseq_1,rc2_finseq_1)).
thf(rc2_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) ) ),file(funcop_1,rc2_funcop_1)).
thf(rc2_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ),file(funct_1,rc2_funct_1)).
thf(rc2_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc2_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc2_xreal_0)).
thf(rc2_xxreal_2,axiom,( ? [A: $i] : ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(xxreal_2,rc2_xxreal_2)).
thf(rc2_zfmisc_1,axiom,( ? [A: $i] : ~ ( v1_zfmisc_1 @ A ) ),file(zfmisc_1,rc2_zfmisc_1)).
thf(rc3_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc3_finseq_1)).
thf(rc3_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ),file(funcop_1,rc3_funcop_1)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
thf(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
thf(rc3_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ~ ( v1_xboole_0 @ C ) ) ) ),file(partfun1,rc3_partfun1)).
thf(rc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relat_1,rc3_relat_1)).
thf(rc3_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc3_xreal_0)).
thf(rc4_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc4_finseq_1)).
thf(rc4_funcop_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(funcop_1,rc4_funcop_1)).
thf(rc4_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc4_funct_1)).
thf(rc4_xreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc4_xreal_0)).
thf(rc5_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc5_finseq_1)).
thf(rc5_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ),file(finset_1,rc5_finset_1)).
thf(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(rc5_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc5_xxreal_2)).
thf(rc6_finseq_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_finseq_1 @ B @ A ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ) ),file(finseq_1,rc6_finseq_1)).
thf(rc6_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ) ),file(finset_1,rc6_finset_1)).
thf(rc6_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(funct_1,rc6_funct_1)).
thf(rc6_valued_0,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v4_valued_0 @ B ) ) ),file(valued_0,rc6_valued_0)).
thf(rc6_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc6_xxreal_2)).
thf(rc7_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc7_finset_1)).
thf(rc7_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) & ~ ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc7_xxreal_2)).
thf(rc8_finseq_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_finseq_1 @ A ) ) ),file(finseq_1,rc8_finseq_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(rc8_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ~ ( v1_xxreal_2 @ A ) & ~ ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc8_xxreal_2)).
thf(rc9_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ),file(finseq_1,rc9_finseq_1)).
thf(rc9_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) ),file(finset_1,rc9_finset_1)).
thf(rc9_funct_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) ),file(funct_1,rc9_funct_1)).
thf(projectivity_k1_card_1,axiom,( ! [A: $i] : ( = @ ( k1_card_1 @ ( k1_card_1 @ A ) ) @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(commutativity_k2_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k2_xcmplx_0 @ A @ B ) @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xcmplx_0,k2_xcmplx_0)).
thf(symmetry_r1_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) & ( v7_topalg_6 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) & ( v7_topalg_6 @ C @ A ) & ( m1_subset_1 @ C @ ( k1_topalg_6 @ A ) ) ) => ( ( r1_topalg_6 @ A @ B @ C ) => ( r1_topalg_6 @ A @ C @ B ) ) ) ),file(topalg_6,r1_topalg_6)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(dt_k1_card_1,axiom,( ! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_m1_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,m1_finseq_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(cc11_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),file(membered,cc11_membered)).
thf(cc13_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(membered,cc13_membered)).
thf(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_membered)).
thf(cc15_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v2_membered @ A ) & ( v6_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc15_xxreal_2)).
thf(cc17_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v2_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v2_valued_0 @ C ) ) ) ),file(valued_0,cc17_valued_0)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
thf(cc18_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v3_membered @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v3_valued_0 @ C ) ) ) ),file(valued_0,cc18_valued_0)).
thf(cc1_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc1_finseq_1)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_funcop_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_funcop_1 @ B ) ) ) ) ),file(funcop_1,cc1_funcop_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_partfun1 @ C @ A ) ) ) ),file(partfun1,cc1_partfun1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc1_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
thf(cc1_topreal6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v2_connsp_1 @ B @ A ) ) ) ) ),file(topreal6,cc1_topreal6)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc1_zfmisc_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,cc1_zfmisc_1)).
thf(cc20_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_membered @ B ) ) ) ),file(membered,cc20_membered)).
thf(cc21_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_membered @ B ) ) ) ),file(membered,cc21_membered)).
thf(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
thf(cc2_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ) ),file(finseq_1,cc2_finseq_1)).
thf(cc2_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc2_finset_1)).
thf(cc2_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ) ),file(funct_1,cc2_funct_1)).
thf(cc2_nat_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ~ ( v3_xxreal_0 @ A ) ) ),file(nat_1,cc2_nat_1)).
thf(cc2_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ~ ( v1_partfun1 @ C @ A ) ) ) ),file(partfun1,cc2_partfun1)).
thf(cc2_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v4_pre_topc @ B @ A ) ) ) ) ),file(pre_topc,cc2_pre_topc)).
thf(cc2_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_relat_1 @ B ) ) ) ),file(relat_1,cc2_relat_1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc2_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc2_xxreal_2)).
thf(cc30_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k1_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v3_valued_0 @ A ) ) ) ),file(valued_0,cc30_valued_0)).
thf(cc31_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_1 @ A @ k5_numbers ) ) => ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(valued_0,cc31_valued_0)).
thf(cc3_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( v5_relat_1 @ B @ A ) ) ),file(finseq_1,cc3_finseq_1)).
thf(cc3_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ) ),file(funcop_1,cc3_funcop_1)).
thf(cc3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_funct_1 @ B ) ) ) ),file(funct_1,cc3_funct_1)).
thf(cc3_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc3_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc3_xxreal_0)).
thf(cc4_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc4_finseq_1)).
thf(cc4_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc4_funct_1)).
thf(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
thf(cc4_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_1)).
thf(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
thf(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(cc4_xxreal_0,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc4_xxreal_0)).
thf(cc5_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc5_finseq_1)).
thf(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc5_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v1_membered @ A ) ) ),file(membered,cc5_membered)).
thf(cc5_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc5_xxreal_0)).
thf(cc5_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc5_xxreal_2)).
thf(cc6_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ) ),file(finseq_1,cc6_finseq_1)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(cc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v5_relat_1 @ C @ A ) ) ) ),file(relat_1,cc6_relat_1)).
thf(cc6_xxreal_0,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc6_xxreal_0)).
thf(cc6_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_finset_1 @ A ) ) => ( ( v3_membered @ A ) & ( v5_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc6_xxreal_2)).
thf(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(cc7_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc7_xxreal_0)).
thf(cc8_finseq_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_finseq_1 @ A ) ) ),file(finseq_1,cc8_finseq_1)).
thf(cc8_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(funct_1,cc8_funct_1)).
thf(cc8_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ( v3_membered @ A ) ) ),file(membered,cc8_membered)).
thf(cc8_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc8_relat_1)).
thf(cc8_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v13_struct_0 @ A @ k1_xboole_0 ) ) ) ),file(struct_0,cc8_struct_0)).
thf(cc8_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) => ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc8_xxreal_0)).
thf(cc9_finset_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) ) ),file(finset_1,cc9_finset_1)).
thf(cc9_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
thf(cc9_topalg_6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) => ( ( v7_topalg_6 @ B @ A ) => ( ( v5_topalg_6 @ B @ A ) & ( v6_topalg_6 @ B @ A ) ) ) ) ) ),file(topalg_6,cc9_topalg_6)).
thf(cc9_valued_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_valued_0 @ A ) ) ) ),file(valued_0,cc9_valued_0)).
thf(fc10_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc10_relat_1)).
thf(fc10_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc10_xreal_0)).
thf(fc11_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc11_xreal_0)).
thf(fc12_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ~ ( v1_subset_1 @ ( k2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc12_struct_0)).
thf(fc12_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v2_xxreal_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc12_xreal_0)).
thf(fc13_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc13_xreal_0)).
thf(fc14_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(finset_1,fc14_finset_1)).
thf(fc14_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc14_xreal_0)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(fc17_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v4_funct_1 @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ C @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ C @ B ) ) ) ) ),file(funct_1,fc17_funct_1)).
thf(fc19_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(finset_1,fc19_finset_1)).
thf(fc1_mfold_2,axiom,( v5_relat_1 @ k1_xboole_0 @ k1_xboole_0 ),file(mfold_2,fc1_mfold_2)).
thf(fc1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( v7_ordinal1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,fc1_nat_1)).
thf(fc1_struct_0,axiom,( ! [A: $i] : ( ( ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc1_struct_0)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc1_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k1_xxreal_2 @ A ) ) & ( v1_xreal_0 @ ( k1_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc1_xxreal_2)).
thf(fc2_mfold_2,axiom,( v2_funct_2 @ k1_xboole_0 @ k1_xboole_0 ),file(mfold_2,fc2_mfold_2)).
thf(fc2_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc2_struct_0)).
thf(fc2_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v3_xxreal_2 @ A ) ) => ( ( v1_xxreal_0 @ ( k2_xxreal_2 @ A ) ) & ( v1_xreal_0 @ ( k2_xxreal_2 @ A ) ) ) ) ),file(xxreal_2,fc2_xxreal_2)).
thf(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(fc3_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,fc3_nat_1)).
thf(fc3_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ B ) => ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(zfmisc_1,fc3_zfmisc_1)).
thf(fc4_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(nat_1,fc4_nat_1)).
thf(fc4_struct_0,axiom,( ! [A: $i] : ( ( ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_xboole_0 @ ( k2_struct_0 @ A ) ) ) ),file(struct_0,fc4_struct_0)).
thf(fc4_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(zfmisc_1,fc4_zfmisc_1)).
thf(fc5_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( k2_struct_0 @ A ) ) ) ),file(struct_0,fc5_struct_0)).
thf(fc5_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc5_xreal_0)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(fc86_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v2_membered @ B ) => ( v2_valued_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(valued_0,fc86_valued_0)).
thf(fc87_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( v3_membered @ B ) => ( v3_valued_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(valued_0,fc87_valued_0)).
thf(fc8_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc8_relat_1)).
thf(fc8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) => ( v1_relat_1 @ ( k9_xtuple_0 @ D ) ) ) ),file(relset_1,fc8_relset_1)).
thf(fc8_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_pre_topc @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) ) => ( v3_membered @ ( k9_xtuple_0 @ B ) ) ) ),file(topalg_6,fc8_topalg_6)).
thf(fc9_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v3_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc9_xreal_0)).
thf(rc1_borsuk_3,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v1_xboole_0 @ B ) ) ) ),file(borsuk_3,rc1_borsuk_3)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc2_finset_1)).
thf(rc2_nat_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) & ~ ( v1_xboole_0 @ A ) & ( v3_ordinal1 @ A ) ) ),file(nat_1,rc2_nat_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc2_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ),file(xxreal_0,rc2_xxreal_0)).
thf(rc3_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc3_finset_1)).
thf(rc3_topalg_6,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v7_topalg_6 @ B @ A ) ) ) ),file(topalg_6,rc3_topalg_6)).
thf(rc3_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(rc4_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(struct_0,rc4_struct_0)).
thf(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(rc4_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc4_xxreal_2)).
thf(rc6_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v4_pre_topc @ B @ A ) ) ) ),file(pre_topc,rc6_pre_topc)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(rc7_pre_topc,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v4_pre_topc @ B @ A ) ) ) ),file(pre_topc,rc7_pre_topc)).
thf(commutativity_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( = @ ( k1_nat_1 @ A @ B ) @ ( k1_nat_1 @ B @ A ) ) ) ),file(nat_1,k1_nat_1)).
thf(projectivity_k3_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( = @ ( k3_finseq_1 @ ( k3_finseq_1 @ A ) ) @ ( k3_finseq_1 @ A ) ) ) ),file(finseq_1,k3_finseq_1)).
thf(reflexivity_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( r1_xxreal_0 @ A @ A ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(connectedness_r1_xxreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( ( r1_xxreal_0 @ A @ B ) | ( r1_xxreal_0 @ B @ A ) ) ) ),file(xxreal_0,r1_xxreal_0)).
thf(symmetry_r2_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( v7_topalg_6 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) & ( v7_topalg_6 @ C @ A ) & ( m1_subset_1 @ C @ ( k1_topalg_6 @ A ) ) ) => ( ( r2_topalg_6 @ A @ B @ C ) => ( r2_topalg_6 @ A @ C @ B ) ) ) ),file(topalg_6,r2_topalg_6)).
thf(reflexivity_r2_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( v7_topalg_6 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) & ( v7_topalg_6 @ C @ A ) & ( m1_subset_1 @ C @ ( k1_topalg_6 @ A ) ) ) => ( r2_topalg_6 @ A @ B @ B ) ) ),file(topalg_6,r2_topalg_6)).
thf(redefinition_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( = @ ( k1_nat_1 @ A @ B ) @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,k1_nat_1)).
thf(redefinition_k3_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( = @ ( k3_finseq_1 @ A ) @ ( k1_card_1 @ A ) ) ) ),file(finseq_1,k3_finseq_1)).
thf(redefinition_k6_numbers,axiom,( = @ k6_numbers @ k1_xboole_0 ),file(numbers,k6_numbers)).
thf(redefinition_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) <=> ( m1_finseq_1 @ B @ A ) ) ),file(finseq_1,m2_finseq_1)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(redefinition_r2_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) & ( v7_topalg_6 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_topalg_6 @ A ) ) & ( v7_topalg_6 @ C @ A ) & ( m1_subset_1 @ C @ ( k1_topalg_6 @ A ) ) ) => ( ( r2_topalg_6 @ A @ B @ C ) <=> ( r1_topalg_6 @ A @ B @ C ) ) ) ),file(topalg_6,r2_topalg_6)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( m2_subset_1 @ ( k1_nat_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(nat_1,k1_nat_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_topalg_6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( m1_subset_1 @ ( k1_topalg_6 @ A ) @ ( k1_zfmisc_1 @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ A ) ) ) ) ) ),file(topalg_6,k1_topalg_6)).
thf(dt_k1_xxreal_2,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ( v1_xxreal_0 @ ( k1_xxreal_2 @ A ) ) ) ),file(xxreal_2,k1_xxreal_2)).
thf(dt_k2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( m1_subset_1 @ ( k2_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),file(struct_0,k2_struct_0)).
thf(dt_k2_xxreal_2,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ( v1_xxreal_0 @ ( k2_xxreal_2 @ A ) ) ) ),file(xxreal_2,k2_xxreal_2)).
thf(dt_k3_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( m2_subset_1 @ ( k3_finseq_1 @ A ) @ k1_numbers @ k5_numbers ) ) ),file(finseq_1,k3_finseq_1)).
thf(dt_k4_partfun1,axiom,( $true ),file(partfun1,k4_partfun1)).
thf(dt_k6_numbers,axiom,( m2_subset_1 @ k6_numbers @ k1_numbers @ k5_numbers ),file(numbers,k6_numbers)).
thf(dt_k6_topalg_6,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_pre_topc @ A ) & ( m1_finseq_1 @ B @ ( k1_topalg_6 @ A ) ) ) => ( m2_subset_1 @ ( k6_topalg_6 @ A @ B ) @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ A ) ) @ ( k1_topalg_6 @ A ) ) ) ),file(topalg_6,k6_topalg_6)).
thf(dt_k7_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( m1_subset_1 @ ( k7_partfun1 @ A @ B @ C ) @ A ) ) ),file(partfun1,k7_partfun1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_l1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( l1_struct_0 @ A ) ) ),file(pre_topc,l1_pre_topc)).
thf(dt_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) => ( ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) ) ) ),file(finseq_1,m2_finseq_1)).
thf(dt_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_c1_80__topalg_6,axiom,( ~ ( v2_struct_0 @ c1_80__topalg_6 ) & ( v2_pre_topc @ c1_80__topalg_6 ) & ( l1_pre_topc @ c1_80__topalg_6 ) ),file(topalg_6,c1_80__topalg_6)).
thf(cc1_borsuk_3,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) ) => ( ( v2_pre_topc @ A ) & ( v1_compts_1 @ A ) ) ) ) ),file(borsuk_3,cc1_borsuk_3)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_topalg_3,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v2_struct_0 @ A ) => ( v1_connsp_1 @ A ) ) ) ),file(topalg_3,cc1_topalg_3)).
thf(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc2_xxreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,cc2_xxreal_0)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc9_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v2_struct_0 @ A ) => ( v6_pre_topc @ A ) ) ) ),file(pre_topc,cc9_pre_topc)).
thf(fc11_xxreal_2,axiom,( ~ ( v3_xxreal_2 @ k1_numbers ) & ~ ( v4_xxreal_2 @ k1_numbers ) ),file(xxreal_2,fc11_xxreal_2)).
thf(fc17_xxreal_2,axiom,( v6_xxreal_2 @ k1_numbers ),file(xxreal_2,fc17_xxreal_2)).
thf(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
thf(fc1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k4_partfun1 @ A @ B ) ) ),file(partfun1,fc1_partfun1)).
thf(fc3_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
thf(fc4_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( v4_funct_1 @ ( k4_partfun1 @ A @ B ) ) ),file(partfun1,fc4_partfun1)).
thf(fc4_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ( v4_pre_topc @ ( k2_struct_0 @ A ) @ A ) ) ),file(pre_topc,fc4_pre_topc)).
thf(fc56_membered,axiom,( v7_membered @ k1_numbers ),file(membered,fc56_membered)).
thf(fc7_topalg_6,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ~ ( v1_xboole_0 @ ( k1_topalg_6 @ A ) ) ) ),file(topalg_6,fc7_topalg_6)).
thf(fc8_numbers,axiom,( ~ ( v1_finset_1 @ k1_numbers ) ),file(numbers,fc8_numbers)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(spc1_numerals,axiom,( ( v2_xxreal_0 @ np__1 ) & ( m2_subset_1 @ np__1 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k1_numbers ) ),file(numerals,spc1_numerals)).
thf(e1_80__topalg_6,axiom,( ! [A: $i] : ( ( m2_finseq_1 @ A @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) => ! [B: $i] : ( ( m2_finseq_1 @ B @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) => ! [C: $i] : ( ( ( v7_topalg_6 @ C @ c1_80__topalg_6 ) & ( m2_subset_1 @ C @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ! [D: $i] : ( ( ( v7_topalg_6 @ D @ c1_80__topalg_6 ) & ( m2_subset_1 @ D @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ( ( ( = @ ( k3_finseq_1 @ A ) @ k6_numbers ) & ( = @ ( k3_finseq_1 @ A ) @ ( k3_finseq_1 @ B ) ) & ( = @ ( k6_topalg_6 @ c1_80__topalg_6 @ A ) @ C ) & ( = @ ( k6_topalg_6 @ c1_80__topalg_6 @ B ) @ D ) & ! [E: $i] : ( ( v7_ordinal1 @ E ) => ( ( r1_xxreal_0 @ np__1 @ E ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ A ) @ E ) | ( ( = @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ A @ E ) @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ A @ E ) ) ) ) @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ A @ ( k1_nat_1 @ E @ np__1 ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ A @ ( k1_nat_1 @ E @ np__1 ) ) ) ) ) ) & ( = @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ A @ E ) ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ A @ ( k1_nat_1 @ E @ np__1 ) ) ) ) ) ) ) ) ) & ! [E: $i] : ( ( v7_ordinal1 @ E ) => ( ( r1_xxreal_0 @ np__1 @ E ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ B ) @ E ) | ( ( = @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ E ) @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ E ) ) ) ) @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ E @ np__1 ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ E @ np__1 ) ) ) ) ) ) & ( = @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ E ) ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ E @ np__1 ) ) ) ) ) ) ) ) ) & ! [E: $i] : ( ( v7_ordinal1 @ E ) => ~ ( ( r1_xxreal_0 @ np__1 @ E ) & ( r1_xxreal_0 @ E @ ( k3_finseq_1 @ A ) ) & ! [F: $i] : ( ( ( v7_topalg_6 @ F @ c1_80__topalg_6 ) & ( m2_subset_1 @ F @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ! [G: $i] : ( ( ( v7_topalg_6 @ G @ c1_80__topalg_6 ) & ( m2_subset_1 @ G @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ~ ( ( = @ F @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ A @ E ) ) & ( = @ G @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ E ) ) & ( r2_topalg_6 @ c1_80__topalg_6 @ F @ G ) & ( = @ ( k9_xtuple_0 @ F ) @ ( k9_xtuple_0 @ G ) ) ) ) ) ) ) ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ A ) @ k6_numbers ) | ( r2_topalg_6 @ c1_80__topalg_6 @ C @ D ) ) ) ) ) ) ) ),file(topalg_6,e1_80__topalg_6)).
thf(e2_80__topalg_6,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ! [B: $i] : ( ( m2_finseq_1 @ B @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) => ! [C: $i] : ( ( m2_finseq_1 @ C @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) => ! [D: $i] : ( ( ( v7_topalg_6 @ D @ c1_80__topalg_6 ) & ( m2_subset_1 @ D @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ! [E: $i] : ( ( ( v7_topalg_6 @ E @ c1_80__topalg_6 ) & ( m2_subset_1 @ E @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ( ( ( = @ ( k3_finseq_1 @ B ) @ A ) & ( = @ ( k3_finseq_1 @ B ) @ ( k3_finseq_1 @ C ) ) & ( = @ ( k6_topalg_6 @ c1_80__topalg_6 @ B ) @ D ) & ( = @ ( k6_topalg_6 @ c1_80__topalg_6 @ C ) @ E ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ( ( r1_xxreal_0 @ np__1 @ F ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ B ) @ F ) | ( ( = @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) ) ) @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) & ( = @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) ) ) ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ( ( r1_xxreal_0 @ np__1 @ F ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ C ) @ F ) | ( ( = @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) ) ) @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) & ( = @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) ) ) ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ~ ( ( r1_xxreal_0 @ np__1 @ F ) & ( r1_xxreal_0 @ F @ ( k3_finseq_1 @ B ) ) & ! [G: $i] : ( ( ( v7_topalg_6 @ G @ c1_80__topalg_6 ) & ( m2_subset_1 @ G @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ! [H: $i] : ( ( ( v7_topalg_6 @ H @ c1_80__topalg_6 ) & ( m2_subset_1 @ H @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ~ ( ( = @ G @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) & ( = @ H @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) & ( r2_topalg_6 @ c1_80__topalg_6 @ G @ H ) & ( = @ ( k9_xtuple_0 @ G ) @ ( k9_xtuple_0 @ H ) ) ) ) ) ) ) ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ B ) @ k6_numbers ) | ( r2_topalg_6 @ c1_80__topalg_6 @ D @ E ) ) ) ) ) ) ) => ! [B: $i] : ( ( m2_finseq_1 @ B @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) => ! [C: $i] : ( ( m2_finseq_1 @ C @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) => ! [D: $i] : ( ( ( v7_topalg_6 @ D @ c1_80__topalg_6 ) & ( m2_subset_1 @ D @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ! [E: $i] : ( ( ( v7_topalg_6 @ E @ c1_80__topalg_6 ) & ( m2_subset_1 @ E @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ( ( ( = @ ( k3_finseq_1 @ B ) @ ( k1_nat_1 @ A @ np__1 ) ) & ( = @ ( k3_finseq_1 @ B ) @ ( k3_finseq_1 @ C ) ) & ( = @ ( k6_topalg_6 @ c1_80__topalg_6 @ B ) @ D ) & ( = @ ( k6_topalg_6 @ c1_80__topalg_6 @ C ) @ E ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ( ( r1_xxreal_0 @ np__1 @ F ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ B ) @ F ) | ( ( = @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) ) ) @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) & ( = @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) ) ) ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ( ( r1_xxreal_0 @ np__1 @ F ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ C ) @ F ) | ( ( = @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) ) ) @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) & ( = @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) ) ) ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ~ ( ( r1_xxreal_0 @ np__1 @ F ) & ( r1_xxreal_0 @ F @ ( k3_finseq_1 @ B ) ) & ! [G: $i] : ( ( ( v7_topalg_6 @ G @ c1_80__topalg_6 ) & ( m2_subset_1 @ G @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ! [H: $i] : ( ( ( v7_topalg_6 @ H @ c1_80__topalg_6 ) & ( m2_subset_1 @ H @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ~ ( ( = @ G @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) & ( = @ H @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) & ( r2_topalg_6 @ c1_80__topalg_6 @ G @ H ) & ( = @ ( k9_xtuple_0 @ G ) @ ( k9_xtuple_0 @ H ) ) ) ) ) ) ) ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ B ) @ k6_numbers ) | ( r2_topalg_6 @ c1_80__topalg_6 @ D @ E ) ) ) ) ) ) ) ) ) ),file(topalg_6,e2_80__topalg_6)).
thf(s2_nat_1,axiom,( ! [A: $i > $o] : ( ( ( A @ k6_numbers ) & ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( ( A @ B ) => ( A @ ( k1_nat_1 @ B @ np__1 ) ) ) ) ) => ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( A @ B ) ) ) ),file(nat_1,s2_nat_1)).
thf(e3_80__topalg_6,conjecture,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ! [B: $i] : ( ( m2_finseq_1 @ B @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) => ! [C: $i] : ( ( m2_finseq_1 @ C @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) => ! [D: $i] : ( ( ( v7_topalg_6 @ D @ c1_80__topalg_6 ) & ( m2_subset_1 @ D @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ! [E: $i] : ( ( ( v7_topalg_6 @ E @ c1_80__topalg_6 ) & ( m2_subset_1 @ E @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ( ( ( = @ ( k3_finseq_1 @ B ) @ A ) & ( = @ ( k3_finseq_1 @ B ) @ ( k3_finseq_1 @ C ) ) & ( = @ ( k6_topalg_6 @ c1_80__topalg_6 @ B ) @ D ) & ( = @ ( k6_topalg_6 @ c1_80__topalg_6 @ C ) @ E ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ( ( r1_xxreal_0 @ np__1 @ F ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ B ) @ F ) | ( ( = @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) ) ) @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) & ( = @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) ) ) ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ( ( r1_xxreal_0 @ np__1 @ F ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ C ) @ F ) | ( ( = @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) ) ) @ ( k1_funct_1 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) & ( = @ ( k1_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) ) @ ( k2_xxreal_2 @ ( k9_xtuple_0 @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ ( k1_nat_1 @ F @ np__1 ) ) ) ) ) ) ) ) ) & ! [F: $i] : ( ( v7_ordinal1 @ F ) => ~ ( ( r1_xxreal_0 @ np__1 @ F ) & ( r1_xxreal_0 @ F @ ( k3_finseq_1 @ B ) ) & ! [G: $i] : ( ( ( v7_topalg_6 @ G @ c1_80__topalg_6 ) & ( m2_subset_1 @ G @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ! [H: $i] : ( ( ( v7_topalg_6 @ H @ c1_80__topalg_6 ) & ( m2_subset_1 @ H @ ( k4_partfun1 @ k1_numbers @ ( k2_struct_0 @ c1_80__topalg_6 ) ) @ ( k1_topalg_6 @ c1_80__topalg_6 ) ) ) => ~ ( ( = @ G @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ B @ F ) ) & ( = @ H @ ( k7_partfun1 @ ( k1_topalg_6 @ c1_80__topalg_6 ) @ C @ F ) ) & ( r2_topalg_6 @ c1_80__topalg_6 @ G @ H ) & ( = @ ( k9_xtuple_0 @ G ) @ ( k9_xtuple_0 @ H ) ) ) ) ) ) ) ) => ( ( r1_xxreal_0 @ ( k3_finseq_1 @ B ) @ k6_numbers ) | ( r2_topalg_6 @ c1_80__topalg_6 @ D @ E ) ) ) ) ) ) ) ) ),file(topalg_6,e3_80__topalg_6)).
